Question

Let's consider several models of the Earth's radiation properties. In each part, assume that the Earth's radiative output balances the input radiation from the Sun, and that there are no other energy or heat sources. 1) Consider a 'far Earth' (FE) that has an orbital distance 1.3 times farther from the sun, but the same diameter as the real Earth (RE). Assume that both are blackbodies with a uniform temperature. What is the ratio of temperatures between those two planets? (Note: you won't need to look up the Earth-Sun distance or the diameter of the Earth) TFE/TRE 2) Now consider just the Earth. Assume that the Earth is a blackbody with a uniform temperature, but now it has a layer of reflecting material, which reflects 25% of light at all frequencies, both for incoming and outgoing light. What is the ratio between the reflecting Earth and the blackbody Earth? Treflecting /Tblackbody Submit

Answer 1

For real earth Total power radiated by the sun = 4 pie R^2_s sigma T^4_s where R_s - radius of sun sigma - Stefan Boltz mann constant T_s - surface temperature of sun per unit area power recieved at eath's distance 4 pie R^2_s sigma T^4_s/4 pie (AU)^2 1 AU - distance between sun & Earth Total Power absorbed by Earth 4 pie R^2_s sigma T^4_s/4 pie (AU)^2 times pie R^2_E Total power radiated by Earth 4 pie R^2_E sigma T^4_E 4 pie R^2_E sigma T^4_E = 4 pie R^2_E R^2_s sigma T^4_s/(AU)^2 For Far earth all other parameters are same just instead of AU we use 1.3 AU \r\n (T_FE/T_RE)^4 = 1/(1.3 AU)^2 1/(AU)^2 T_FE/T_RE = 1/squareroot 1.3 = 0.8771 if 25% of power incident is reflected then absorbed power would be from equation 1 0.75 R^2_s sigma T^4_s/(AU)^2 times pie R_E^2 & power radiated 0.75 times p